Electron density measurement and plasma process control system using changes in the resonant frequency of an open resonator containing the plasma

ABSTRACT

A system for measuring plasma electron densities (e.g., in the range of 1010 to 1012 cm−3) and for controlling a plasma generator. Measurement of the plasma electron density is used as part of a feedback control in plasma-assisted processes, such as depositions or etches. Both the plasma measurement method and system generate a control voltage that in turn controls the plasma generator. A programmable frequency source sequentially excites a number of the resonant modes of an open resonator placed within the plasma processing apparatus. The resonant frequencies of the resonant modes depend on the plasma electron density in the space between the reflectors of the open resonator. The apparatus automatically determines the increase in the resonant frequency of an arbitrarily chosen resonant mode of the open resonator due to the introduction of a plasma and compares that measured frequency to data previously entered. The comparison is by any one of (1) dedicated circuitry, (2) a digital signal processor, and (3) a specially programmed general purpose computer. The comparator calculates a control signal which is used to modify the power output of the plasma generator as necessary to achieve the desired plasma electron density.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is related to co-pending applications entitled“ELECTRON DENSITY MEASUREMENT AND PLASMA PROCESS CONTROL SYSTEM USING AMICROWAVE OSCILLATOR LOCKED TO AN OPEN RESONATOR CONTAINING THE PLASMA,”Ser. No. 60/144,878 and “ELECTRON DENSITY MEASUREMENT AND PLASMA PROCESSCONTROL SYSTEM USING A MICROWAVE OSCILLATOR LOCKED TO AN OPEN RESONATORCONTAINING THE PLASMA,” Ser. No. 60/144,880 both of which have beenfiled concurrently herewith. Both of those applications are hereinincorporated by reference in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention provides a method and system for measuring andcontrolling electron densities in a plasma processing system, such as isused in semiconductor processing systems.

2. Description of the Background

Known microwave-based techniques for determining plasma electrondensities include: (1) microwave interferometry, (2) measurement ofreflection and absorption, and (3) perturbation of cavity resonantfrequencies. Microwave interferometry involves the determination of thephase difference between two microwave beams. The first beam provides areference signal, and the second beam passes through a reactiveenvironment and undergoes a phase shift relative to the first beam. Theindex of refraction is calculated from the measured change in the phasedifference between the two beams. The interferometric technique has beendocument by Professor L. Goldstein of the University of Illinois atUrbana. Interferometry is described in the following U.S. Pat. Nos.:2,971,153; 3,265,967; 3,388,327; 3,416,077; 3,439,266; 3,474,336;3,490,037; 3,509,452; and 3,956,695, each of which is incorporatedherein by reference. Examples of other non-patent literature describinginterferometry techniques include: (1) “A Microwave Interferometer forDensity Measurement Stabilization in Process Plasmas,” by Pearson etal., Materials Research Society Symposium Proceedings, Vol. 117 (Eds.Hays et al.), 1988, pgs. 311-317, and (2) “1-millimeter waveinterferometer for the measurement of line integral electron density onTFTR,” by Efthimion et al., Rev. Sci. Instrum. 56 (5), May 1985, pgs.908-910. Some plasma properties may be indirectly determined frommeasurements of the absorption of a microwave beam as it traverses aregion in which a plasma is present. Signal reflections in plasmas aredescribed in U.S. Pat. Nos. 3,599,089 and 3,383,509.

Plasma electron densities have also been measured using a techniquewhich measures the perturbations of cavity resonant frequencies. Thepresence of a plasma within a resonator affects the frequency of eachresonant mode because the plasma has an effective dielectric constantthat depends on plasma electron density. This technique has beendocumented by Professor S. C. Brown of the Massachusetts Institute ofTechnology. Portions of this technique are described in U.S. Pat. No.3,952,246 and in the following non-patent articles: (1) Haverlag, M., etal., J. Appl Phys 70 (7) 3472-80 (1991): Measurements of negative iondensities in 13.56 MHZ RF plasma of CF₄, C₂F₆. CHF₃, and C₃F₈ usingmicrowave resonance and the photodetachment effect; and (2) Haverlag,M., et al., Materials Science Forum, vol. 140-142, 235-54 (1993):Negatively charged particles in fluorocarbon RF etch plasma: Densitymeasurements using microwave resonance and the photodetachment effect.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a more accurateplasma measuring system than the prior art.

It is a further object of the present invention to provide an improvedplasma measuring system using plasma induced changes in the frequenciesof an open resonator.

These and other objects of the present invention are achieved using avoltage-controlled programmable frequency source that sequentiallyexcites a number of the resonant modes of an open resonator placedwithin the plasma processing apparatus. The resonant frequencies of theresonant modes depend on the plasma electron density in the spacebetween the reflectors of the open resonator. The apparatusautomatically determines the increase in the resonant frequency of anarbitrarily chosen resonant mode of the open resonator due to theintroduction of a plasma and compares that measured frequency to datapreviously entered. The comparison is by any one of (1) dedicatedcircuitry, (2) a digital signal processor, and (3) a speciallyprogrammed general purpose computer. The comparator calculates a controlsignal which is used to modify the power output of the plasma generatoras necessary to achieve the desired plasma electron density.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof will become readily apparent with reference to thefollowing detailed description, particularly when considered inconjunction with the accompanying drawings, in which:

FIG. 1 is a schematic illustration of a computer system for implementingthe measurement and control of the present invention;

FIG. 2 is a graph of the sequential excitation of the modes of an openresonator by the sweep of the frequency of the programmable frequencysource while the resonant frequencies of the modes are being shifted dueto the formation of the plasma;

FIG. 3 is a block diagram of a circuit for measuring and controllingplasma electron density according to the present invention;

FIG. 4 is a graph that is similar to FIG. 2, but without the presence ofthe plasma shifting the resonances to higher frequencies;

FIGS. 5A and 5B are graphs that illustrate the problems with anon-monotonic change in the plasma electron density; and

FIG. 6 is a graph of the sequential excitation of the modes of an openresonator by sweeping the frequency of the programmable frequency sourcea number of times in series while the resonant frequencies of the modesare being shifted due to the formation of the plasma.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views, FIG. 1 isa schematic illustration of an embodiment of a measurement and controlsystem, according to the present invention, for a plasma processingsystem. In this embodiment, a computer 100 implements the method of thepresent invention, wherein the computer housing 102 houses a motherboard104 which contains a CPU 106, memory 108 (e.g., DRAM, ROM, EPROM,EEPROM, SRAM and Flash RAM), and other optional special purpose logicdevices (e.g., ASICs) or configurable logic devices (e.g., GAL andreprogrammable FPGA). The computer 100 also includes plural inputdevices, (e.g., a keyboard 122 and mouse 124), and a display card 110for controlling monitor 120. In addition, the computer system 100further includes a floppy disk drive 114; other removable media devices(e.g., compact disc 119, tape, and removable magneto-optical media (notshown)); and a hard disk 112, or other fixed, high density media drives,connected using an appropriate device bus (e.g., a SCSI bus, an EnhancedIDE bus, or an Ultra DMA bus). Also connected to the same device bus oranother device bus, the computer 100 may additionally include a compactdisc reader 118, a compact disc reader/writer unit (not shown) or acompact disc jukebox (not shown). Although compact disc 119 is shown ina CD caddy, the compact disc 119 can be inserted directly into CD-ROMdrives which do not require caddies. In addition, a printer (not shown)also provides printed listings of frequency graphs showing resonantfrequencies of the open resonator.

As stated above, the system includes at least one computer readablemedium. Examples of computer readable media are compact discs 119, harddisks 112, floppy disks, tape, magneto-optical disks, PROMs (EPROM,EEPROM, Flash EPROM), DRAM, SRAM, SDRAM, etc. Stored on any one or on acombination of computer readable media, the present invention includessoftware for controlling both the hardware of the computer 100 and forenabling the computer 100 to interact with a human user. Such softwaremay include, but is not limited to, device drivers, operating systemsand user applications, such as development tools. Such computer readablemedia further include the computer program product of the presentinvention for controlling a plasma processing system. The computer codedevices of the present invention can be any interpreted or executablecode mechanism, including but not limited to scripts, interpreters,dynamic link libraries, Java classes, and complete executable programs.

In an alternate embodiment, the computer 100 includes a digital signalprocessor (not shown) for performing signal processing on receivedinputs. In yet another alternate embodiment, the CPU 106 is programmedwith software to perform digital signal processing routines analogous tothe Internal operation of a DSP. In a further embodiment, the computer100 is replaced by a DSP and memory (e.g., on a printed circuit board)for performing the operations of the computer described herein.Likewise, the functions of the DSP may be replaced by dedicated analogand/or digital circuitry for performing the operations described herein.

As shown in FIG. 3, the computer 100 is programmed to measure a plasmaelectron density and control a programmable frequency source (PFS) 201.One embodiment of a programmable frequency source includes a D/Aconverter coupled to a voltage-controlled frequency modulated microwaveoscillator. However, the frequencies applied by the programmablefrequency source 201 depend on the behavior of the resonant frequenciesof the open resonator modes as the plasma is established by the plasmagenerator 320. For purposes of the description of FIG. 2, it is assumedthat the plasma electron density increases monotonically from itsinitial value to its final value (e.g., 2×10¹² cm⁻³). As a non-limitingexample, it is also assumed that the mode spacing in the empty (i.e.,evacuated) resonator 305 is approximately c/2d=500 MHZ, where c is thespeed of light in vacuum and d is the reflector spacing, i.e., thespacing between the reflectors. As shown in FIG. 2, the mode spacingwith the plasma present is c/(2nd), where n is the index of refraction.If the index of refraction is not uniform as a function of position, nmay be replaced by <n>, its mean value along an appropriate path betweenthe reflectors. The spacing is not quite uniform because the index ofrefraction depends very slightly on the frequency as well as on theplasma electron density and spurious sources of phase shift associatedwith the coupling apertures.

To control the plasma processing system, the system determines a finaloperating frequency at which the system is to operate to establish andmaintain a desired plasma electron density. The final operatingfrequency is determined as follows. At the time T₀, just as the plasmabegins to form, the computer 100 sets the frequency of the programmablefrequency source 201 to a predetermined maximum frequency, f_(max)(e.g., 38.75 GHz). The computer 100 then decreases the frequency withrespect to time (e.g., by changing a digital control signal output bythe computer 100). In the illustrated embodiment, the decrease islinear, but in practice, the decrease can be either linear ornon-linear, but in either case, it should be repeatable and thuspredicatable. The frequency of the programmable frequency source 201 isdecreased until it reaches a minimum frequency, f_(min), (e.g., 36.75GHz) at the time T₁, which is just after the plasma has essentiallyattained its steady-state density 2×10¹² cm⁻³. The selection of thefrequencies f_(max) and f_(min) are somewhat arbitrary. They are chosenin the microwave spectrum and about a nominal frequency convenient formicrowave apparatus, i.e., ˜35 GHz. If the maximum frequency has beenarbitrarily chosen to be 38.75 Ghz, then choosing f_(min) to be 36.75Ghz is such that eight resonant modes are observed over the frequencyrange f_(min)<f<f_(max) in the resonant cavity without a plasma. Theminimum number of modes scanned is determined by (1) the method ofsweeping the frequency (with linear or non-linear changes) with time and(2) the time over which the frequency is swept. Furthermore, themicrowave apparatus can have a range within which it may be varied(limited by hardware constraints). The time over which the frequency isswept should be greater than the plasma adjustment period (formationtime T₁−T₀) to give meaningful results. The sweep time scale includesthe decreasing and increasing sweeps. In a first embodiment, R isassumed that the plasma electron density between times T₀ and T₁ ismonotonically increasing so that number of modes passed while increasingor decreasing the sweeping frequency is counted property.

Generally, the resonances are indicated by a greatly enhanced value ofthe transmitted microwave energy and are counted as the frequency of theprogrammable frequency source 201 is decreased over the defined range.Likewise, when increasing the frequency from the programmable frequencysource 201 over the defined range, the modes are counted and correlatedwith the modes counted during the decrease. During the decrease infrequency, the system detects the appearance of resonant frequencies inthe open resonator and records the frequencies of the oscillator whichproduced the resonant frequencies. FIG. 2 is a graph of the sequentialexcitation of the modes of an open resonator by the sweep of thefrequency of the programmable frequency source while the resonantfrequencies of the modes are being shifted due to the formation of theplasma. In the example of FIG. 2, eight resonances of the open resonatorare excited as the frequency of the programmable frequency source 201decreases from its maximum frequency, f_(max), to its minimum frequency,f_(min).

Having decreased the programmable frequency source 201 to its minimumfrequency, the system then increases the frequency of the programmablefrequency source 201 with respect to time until, at the time T₂, thefrequency again reaches the maximum frequency, f_(max). As during thedecrease, resonant frequencies are detected and recorded, and theincrease may either be linear, as shown in FIG. 2, or non-linear withrespect to time. The time between T₁ and T₂ is called the retrace time.During the retrace time of FIG. 2, four resonant frequencies of the openresonator are excited. The system determines the difference between thenumber of resonant frequencies during the decrease and the increase.This difference is the integer part of a characteristic called thefringe order. In the example of FIG. 2, the difference is four.

The fractional part of the fringe order is obtained in part from thedifference between (a) the frequency, f_(final), of the final resonantfrequency excited (e.g., f_(final)=38.644 GHz in FIG. 2) and (b) thehighest resonant frequency of the empty open resonator that is also lessthan f_(final). In this case, that frequency, f_(open), is 38.500 GHz,and is determined by performing a calibration, run apriori to determinethe mode spacing and the frequencies of the resonant modes. Calibrationis done when no plasma is present within the chamber. This is anaccurate measurement and check of the mode spacing given by c/2d and theresonant frequencies present when there exists no plasma (i.e.,f(q)=(c/2d)(q+½)). The difference is divided by the mode spacing of theempty open resonator (e.g., 0.5 GHz). Thus, the fractional part of thefringe order is given by:$\frac{f_{final} - f_{open}}{{mode}\quad{spacing}} = {\frac{38.644 - 38.5}{0.5} = 0.288}$The entire fringe order is then 4.288, and the frequency shift of themode is 4.288×(mode spacing)=4.288×0.500 GHz =2.144 GHz.

Just as the system calculates the open resonant frequency, f_(open),below the final frequency, f_(final), the system also determines theopen resonator frequency, f_(omin), just below the minimum frequency,f_(min). The value of the index of refraction in the steady-statecondition is then calculated according to:$\frac{f_{omin}}{f_{final}} = {\frac{36.5}{38.644} = {0.945.}}$

A more concrete example is explained hereafter with reference to FIG. 2.Starting from a point on the mode characteristic for which the resonantfrequency is 38.644 GHz (near the right side of FIG. 2) an imaginaryline is drawn down to the dashed horizontal line at 38.500 GHz. Thisdrop corresponds to a frequency change of 0.144 GHz. Then, when movingto the left to the axis of ordinates along the 38.500 GHz line, there isa drop of four mode spaces of the empty open resonator, i.e., 4×0.500GHz =2.000 GHz, to reach 36.500 GHz. Note that 36.500 GHz is thestarting resonant frequency of the mode characteristic that ends with aresonant frequency of 38.644 GHz. It should be noted that a one-to-onecorrespondence exists between the frequency vs. time plot of FIG. 2 anda plot of the voltage controlling the programmable frequency source 201vs. time. Thus, it is quite reasonable to interpolate between theseveral curves in the manner described herein.

In an alternate embodiment, if the plasma electron density does notincrease monotonically during the period when the plasma forms, theprocedure described above is modified. The decrease in the frequency ofthe programmable frequency source 201 during the time period between T₀and T₁ must be controlled in such a way that no mode of the openresonator is excited more than once. Likewise, during the retrace timebetween T₁ and T₂, the increase in the frequency of the programmablefrequency source 201 is controlled so that no mode of the open resonatoris excited more than once. FIGS. 5A and 5B Illustrate non-monotonicallychanging curves which are analyzed differently than the monotonicallychanging curves. FIG. 5A illustrates that it is improper to count thesame mode more than once. Likewise, FIG. 5B shows it is improper tocount a mode during the increase of the frequency of the programmablefrequency source 201 that was not counted during the decrease of theswept frequency.

A first technique to assure that no mode is counted more than once whilethe frequency of the programmable frequency source 201 is decreasing ormore than once while the frequency of the programmable frequency source201 is increasing depends on the relationship between the slope of theopen resonator mode frequency characteristics, df_(orm)/dt, and theslope of the frequency characteristic, df_(PFS)/dt, where t is the time,of the programmable frequency source 201. FIG. 2 illustrates thesignificance of the times to which references are made below.

T₀<t<T. The slope of the PFS frequency characteristic, df_(PFS)/dt is tobe more negative than the most negative value of the slope of any openresonator mode frequency characteristic, df_(orm)/dt, which itintersects.

T₁<t<T₂. The slope of the PFS frequency characteristic, df_(PFS)/dt, isto be more positive than the most positive value of the slope of anyopen resonator mode frequency characteristic, df_(orm)/dt, which itintersects.

As indicated in FIG. 2, ft is presumed that the steady-state conditionhas been attained by the time T₁.

It is well known that the index of refraction n and the plasma electrondensity N may be related to one another by the following approximateformula:${n = {\sqrt{1 - \frac{{Ne}^{2}}{ɛ_{0}{m\left( {2\pi\quad f} \right)}^{2}}} = \sqrt{1 - \left( \frac{f_{p}}{f} \right)^{2}}}},$where e is the magnitude of the charge of an electron, m is the mass ofan electron, ε_(o), is the permittivity of free space, and f_(p) is theplasma frequency. If the equation:$\left( \frac{f_{p}}{f} \right)^{2} \in 1$also is true, which it is in the example, it follows that:$n = {1 - {\frac{e^{2}}{8\pi^{2}ɛ_{0}{mf}^{2}}N}}$and $N = {\frac{8\pi^{2}ɛ_{0}{mf}^{2}}{e^{2}}{\left( {1 - n} \right).}}$

As discussed above, if the index of refraction is not uniform as afunction of position, n may be replaced by <n>, its mean value along anappropriate path between the reflectors, and N becomes <N>, itscorresponding mean value.

Returning now to the description of FIG. 3, FIG. 3 shows the computer ofFIG. 1 as part of the overall plasma processing system. The frequency ofthe programmable frequency source 201 is controlled by the computer 100by varying a digital output signal applied to the programmable frequencysource 201. (In an alternate embodiment of the present invention, theprogrammable frequency source 201 receives an analog input, in whichcase the computer 100 includes or is connected to a digital-to-analogconvertor for providing the analog signal to the programmable frequencysource 201.) The PFS 201 is connected to an isolator 210 a whichisolates the programmable frequency source 201 from the plasma chamber300. The isolator 210 a couples an output signal through an iris 310 bof an open resonator 305 contained with the plasma chamber 300. Thesignal reflected back through the iris 310 a is coupled to a peakdetector 260.

During operation of one embodiment, the computer 100 samplestime-dependent inputs from the plasma chamber 300, the plasma generator320, and a counter 250. (In an alternate embodiment, the counter 250 ismoved internal to the computer 100 and the computer uses the output ofthe peak detector 260 to detect peaks directly—e.g., using interrupts.)Between time T₀ and time T₁, each time a resonance frequency of the openresonator 305 is excited, a peak in the reflected microwave signal ofthe open resonator 305 is detected. This peak increases a count of thecounter 250 which counts a number of peaks since the last reset signal.Thus, as the frequency of the PFS 201 decreases, the number of modesexcited is counted and stored, either in the counter 250 or in thecomputer 100. For the graph shown in FIG. 2, the count would be eight.After the time T₁, when the PFS frequency begins to Increase, the countof the number of resonances as the frequency of the PFS increases ismade. For the graph shown in FIG. 2, the count would be four. When thePFS has returned to its maximum frequency, f_(max) (e.g., 38.75 GHz InFIG. 2), the computer 100 begins a search procedure with the aid of thepeak detector 280 to return to the final resonance detected. Thecomputer 100 then locks on to f_(final) with the aid of the peakdetector 260 and appropriate software. The frequency f_(final) ismeasured and stored.

Having determined the number of detected resonance frequencies detectedbetween T₀ and T₁ and between T₁ and T₂, the computer 100 calculates thefringe order (e.g., 4.288). In order to calculate the correspondingfrequency shift, however, the computer 100 also needs the frequencydifference between adjacent modes for the empty open resonator, i.e.,the mode spacing.

The mode spacing is obtained in advance during a calibration processthat is similar to the procedure by which the fringe order was obtained.FIG. 4, which is similar to FIG. 2, depicts, for the resonancefrequencies in an empty open resonator, the modal characteristics whichare horizontal and spaced 500 MHz apart for the example consideredherein. At the time T₀, the frequency of the PFS 201 is decreased andthen, at the time T₁, the frequency begins to return to its steady-statevalue. In this case, however, the computer 100 (1) counts the number ofmodes excited as the frequency decreases, (2) locks on to the first modedetected, and (3) records the locked frequency. After the frequency hasstarted to increase, the computer 100 searches for and locks on to thefinal resonance frequency detected with the aid of the peak detector 260and appropriate software. The computer 100 also measures and stores thefinal resonance frequency detected.

Based on the data collected during the calibration process and the datasampled during operation, the computer 100 calculates the mode spacingsfor the empty open resonator 305 and the frequency associated with eachresonance for frequencies of interest here.

A more detailed description of the sequence of operations of theapparatus is described below.

(1) As on optional preliminary step, an equipment operator may elect tomonitor that the programmable frequency source is operating withinspecifications. However, if the operator is confident that the system isoperating correctly, this step can be omitted.

(2) The equipment operator then selects the operating parameters underwhich the plasma chamber 300 is to operate. The parameter and thesequence of operation are selected via a data input device (e.g.,keyboard 122, mouse 124, or other control panel). The parametersinclude, but are not limited to, one or more of the following: a desiredplasma electron density, a desired index of refraction, the processduration, and the gas to be used.

(3) After having entered all required data, the operator initiates theprocess through a data input device.

(4) The computer 100 controls the calibration of the empty openresonator as described above.

(5) The computer 100 controls ignition of a plasma in the open resonator305. As the plasma forms, the computer 100 evaluates (1) inputs (e.g.,reflected power) sent to it from the plasma generator 320 and (2) Inputs(e.g., optical emissions) sent to it from the plasma chamber 300. Thecomputer 100 controls the frequency of the PFS 201 as described abovewith reference to FIG. 2.

(6) The computer 100 calculates the fringe order.

(7) The computer 100 calculates the index of refraction n or <n>.

(8) The computer 100 calculates the plasma electron density N or <N>.

(9) The computer 100 compares the measured/calculated plasma electrondensity with the value previously entered by the operator at theoperator entry port.

(10) The computer 100 sends a control signal to the plasma generator 320to change its output as necessary to maintain the desired plasmaelectron density.

(11) The computer 100 repeats steps (6)-(10) throughout the process tokeep the plasma electron density at the desired level.

In addition to the above uses, the system must also accommodate anoperators desire to return the system to another state at an arbitrarytime. For example, the equipment operator may determine that theelectron (plasma) concentration is not optimum for the intended purposeand may want to adjust the concentration. The procedure to be followedwill depend on the technique used to track open resonator modes duringstart-up. The operator enters, by means of a control console (eitherlocal or remote), the value of the desired end parameter (mean index ofrefraction, electron density, etc., depending on the design of thecontrol console) to be modified.

Although the above description was given assuming a simplified frequencyresponse during plasma initiation, such a response may not occur. Asecond technique assures that no mode is counted more than once whilethe frequency of the programmable frequency source 201 is decreasing ormore than once while the frequency of the programmable frequency source201 is increasing. The second technique is similar to the firsttechnique described above but uses a different sweeping technique. Thefrequency of the programmable frequency source 201 is decreased andincreased sequentially a number of times during the time from T₀ to T₂,as shown in FIG. 6. The sweep can be either periodic or aperiodic. Thedependence of the frequency of the programmable frequency source 201 ontime is such that the slope of the frequency characteristic satisfiescriteria analogous to those enumerated above for the first technique.That is, when the slope of the frequency characteristic, df_(PFS)/dt, isnegative, it is to be more negative than the most negative value of theslope of any open resonator mode frequency characteristic, df_(orm)/dt,which it intersects. Likewise, when the slope of the frequencycharacteristic, df_(PFS),/dt, is positive, it is to be more positivethan the most positive value of the slope of any open resonator modefrequency characteristic, df_(orm)/dt, which it intersects. These slopeconditions are, in general, more easily satisfied in this secondtechnique than in the first, because the time increments during whichthe frequency of the programmable frequency source 201 decreases orincreases are only a small fraction of the time interval between T₀ andT₂.

In this second technique the modes are counted as in the first techniquebut for the entire sequence of frequency sweeps. After the steady-stateplasma electron density has been attained, the fractional part of thefringe order is determined as described previously for a monotonicallyincreasing plasma electron density.

A third technique employs a frequency-time characteristic of theprogrammable frequency source 201 such that during start-up no mode isexcited in the open resonator in the time interval between T₀ and T₂, asshown in FIG. 2. Such a frequency-time characteristic corresponds to nomode shift; i.e., the integer part of the fringe order is zero and neednot be considered further. The fractional part of the fringe order canbe determined as described previously for a monotonically increasingplasma electron density.

The implementation of this technique requires that the computer 100 beprogrammed to provide a suitable frequency-time characteristic. Anappropriate program can be determined empirically by examining the modeexcitations during start-up and changing the program to eliminate themone-by-one, starting with the one first excited after start-up begins.

If the equipment uses the first or second technique to identify modechanges as described above, the PFS sweep is reinitiated and thecalibration data and start-up mode data stored in the computer from theimmediately preceding start-up are used by the computer to calculate theconsequent end parameter change. Such an end parameter may, for example,correspond to an plasma electron density. The computer starts the PFSsweep immediately before it begins to respond to the changed input data.The amount of lead time depends on the various response times of theequipment

Using the techniques described above, the system can track mode changesgenerally using a PFS sweep. The system thus determines both the integerand fractional part of any consequent fringe change.

The accuracy of this procedure is limited by the accuracy with which thefrequencies involved in the calculations can be measured. The systemessentially calculates the index of refraction n or <n> from thedifferences of measured frequencies, and these may be difficult tomeasure with an accuracy better than 0.05%. If this is the case, theindex of refraction may be accurate only to about 0.10%, because it iscalculated from the ratio of two measured frequencies. Assuming that theindex of refraction for a particular case is actually 0.93 (whichcorresponds to a plasma electron density on the order of 1×10¹² cm⁻³),the measured value might be expected to lie between 0.929 and 0.931. Theplasma electron density is proportional to (1−n) which lies between0.069 and 0.071 for the example of FIG. 2. Thus, the accuracy with whichthe plasma electron density may be determined is on the order of0.001/0.070=1.4%.

As would be evident to one of ordinary skill in the art, the greater thenumber of modes swept without a plasma, the better the resolution androbustness of the system.

Obviously, numerous modifications and variations of the presentinvention are possible in light of the above teachings. It is thereforeto be understood that, within the scope of the appended claims, theinvention may be practiced otherwise than as specifically describedherein.

1. A system for measuring a plasma electron density in a plasma chamber,the system comprising: a plasma chamber containing a plasma; a frequencysource for providing a signal to the plasma chamber such that the signalsweeps in decreasing frequency direction and then sweeps in anincreasing frequency direction; a resonance frequency detector fordetecting a first set of resonance frequencies excited by the decreasingfrequency sweep and detecting a second set of resonance frequenciesexcited by the increasing frequency sweep; a comparator for determininga difference between a number of frequencies in the first and secondsets; a fringe order calculator for determining a fringe order of theplasma; and a density calculator for determining a plasma electrondensity of the plasma based on the fringe order.
 2. The system accordingto claim 1, wherein the frequency source comprises a voltage-controlledmicrowave oscillator.
 3. The system according to claim 2, wherein thefrequency source further comprises a digital-to-analog convertor forapplying a voltage to the voltage-controlled microwave oscillator. 4.The system according to claim 1, wherein the plasma chamber comprises anopen resonator immersed in a plasma.
 5. The system according to claim 4,wherein the open resonator comprises plural reflectors, wherein allinput and output connections are made to only one of the pluralreflectors.
 6. The system according to claim 1, further comprising adata input device for entering a desired plasma electron density.
 7. Thesystem according to claim 6, further comprising: a plasma generator; andan automatic controller for controlling the plasma generator to producethe desired plasma electron density based on the density calculated bythe density calculator.
 8. A method for measuring a plasma electrondensity in a plasma chamber, the method comprising the steps of: (a)sweeping a signal output from a frequency source in a decreasingfrequency direction and providing the decreasing frequency sweep signalto the plasma chamber; (b) sweeping the signal of the frequency sourcein an increasing frequency direction and providing the increasingfrequency sweep signal to the plasma chamber after providing thedecreasing frequency sweep signal; (c) detecting, via a resonancefrequency detector, a first set of resonance frequencies excited by thedecreasing frequency sweep; (d) detecting, via the resonance frequencydetector, a second set of resonance frequencies excited by theincreasing frequency sweep; (e) determining a difference between anumber of frequencies in the first and second sets; (f) calculating afringe order of the plasma; and (g) determining a plasma electrondensity of the plasma based on the fringe order.
 9. The method accordingto claim 8, wherein the steps (a) and (b) comprise providing frequenciesvia a voltage-controlled microwave oscillator.
 10. The method accordingto claim 8, wherein the steps (a) and (b) comprise providing frequenciesto an open resonator immersed in a plasma.
 11. The method according toclaim 10, wherein the steps (c) and (d) comprise detecting from pluralreflectors, wherein all input and output connections are made to onlyone of the plural reflectors.
 12. The method according to claim 8,further comprising the step of inputting a desired plasma electrondensity.
 13. The method according to claim 12, further comprising thesteps of: generating a plasma in a plasma generator; and controlling theplasma generator to produce the desired plasma electron density based onthe density calculated by the density calculator.